Find the first five non-zero terms of power series representation centered at x=0 for the function below.
f(x)=7/(1−x^2)

Question

Find the first five non-zero terms of power series representation centered at x=0 for the function below.
f(x)=7/(1−x^2)

anonymous · Answer

I found the formula, I'm just really confused on finding the first five terms

anonymous · Answer

7 * series from n=0 to infinity of x^(2n)

anonymous · Answer

sure!

anonymous · Answer

the first thing i would do is factor out 7

anonymous · Answer

I think I did...? idk

anonymous · Answer

$$ 
\Large {
\frac{7}{1-x^2}= 7\cdot \frac{1}{1-x^2}=  7 \sum_{k=0}^{n}x^{2k} 

}

$$

anonymous · Answer

OH yup! That's what I got!

anonymous · Answer

Okay, I realized I just left the n.

anonymous · Answer

Okay thank you :)

anonymous · Answer

$$ 
\Large {
\frac{7}{1-x^2}\= 7\cdot \frac{1}{1-x^2}=  7 \sum_{k=0}^{n}x^{2k} 
\ = 7 ~(x^{2 \cdot 0 } + x^{2\cdot 1} + x^{2\cdot 2} + x^{2\cdot 3}+x^{2\cdot 4}...   ) 
\ = 7 ~(1 + x^2 + x^4 + x^{6}+x^8...   ) 
\ = 7 + 7x^2 + 7x^4 + 7x^6 +7x^8... 
\
}

$$

anonymous · Answer

your welcome